Problem
GEO-B2-M05-P010 Line into a Circle
#10
★★★☆☆ Level 3 of 5
Points \(A',B',C'\) lie on a line not passing through \(O\). Let \(A,B,C\) be their preimages. Prove that \(O,A,B,C\) lie on one circle.
Inversion is its own inverse.
A line not passing through the centre maps to a circle through the centre. Hence the preimages of \(A',B',C'\) lie on one circle with point \(O\). Therefore \(O,A,B,C\) are concyclic.
The converse direction to the previous problem.